This invention relates generally to systems for measuring turbine exhaust gas temperatures and more particularly to a method and sensors for accurately measuring deviations in the exhaust gas temperature profile of a turbine.
Turbines, including gas, steam and other forms of turbomachinery, include a stator structure and a rotor structure. The stator is a fixed structure around which the rotor rotates. The stator and rotor each generally includes one or more sets of blades offset from one another and extending into an annular flow path between the stator and the rotor. In a gas turbine, for example, a set of stator compressor blades and a set of rotor compressor blades act together to compress air entering the flow path. Fuel is injected into the flow path beyond the compressor blades. Mixing nozzles in the flow path act to mix the fuel and compressed air in a premixing stage. That mixture is then ignited in a combustor stage. The product of combustion is an expanded gas that passes through the flow path of the turbine to contact a set of stator turbine blades and a set of rotor turbine blades. The expanded gas moving in the flow path acts to move the rotor turbine blades, causing their rotation. Spent combustion products exit the turbine as exhaust gas directed to the atmosphere by an exhaust duct.
An important operating and control parameter associated with efficient turbine operation is the temperature of the exhaust gas. Typically, the exhaust gas is measured using a plurality of thermocouples spaced equidistant around the circumference of the exhaust duct. The mean exhaust temperature calculated from the retrieved thermocouple measurements is used to monitor and control turbine operation. In addition, deviations in temperature readings between individual thermocouples are monitored for undesirable operating conditions and events. Relatively small deviations may be evidence of operating inefficiencies placing uneven stress in localized areas of the turbine, thereby reducing service life of one or more components. Large temperature deviations may be evidence of serious abnormalities requiring immediate attention.
Statistical evidence gathered from thermocouple outputs over many hours of turbine operation has generally been used to establish failure trends. It has been determined that such statistical trending has been a useful diagnostic tool for incipient failure detection. Measured temperature deviations have been used to detect anomalies including, but not limited to, fuel nozzle defects, combustor stage liner cracking, turbine flame out, fuel/air premixing flashback, and/or structural leakage. All such anomalies influence the rates at which fuel and/or air are introduced into the turbine and so their detection is of great importance.
Difficulties arise in such monitoring and diagnostic techniques resulting from a masking of the abnormalities that the thermocouples are designed to detect. Specifically, the thermocouples are ordinarily laid out circumferentially around the exhaust duct in pre-determined patterns defined by the number, location, and spacing of the combustor elements and the stator and rotor blades. These difficulties can often be traced to a phenomenon known as aliasing. In general terms, aliasing occurs when sampling intervals are insufficient to distinguish between events taking place at different frequencies. That is, a sampling rate may be sufficient to detect events at one frequency but insufficient to detect events occurring at a higher frequency. Of greater concern, normal high frequency events may appear as low frequency signals, thereby masking anomalous low-frequency events.
In the context of a turbine exhaust duct, aliasing occurs when normally occurring exhaust temperature patterns include high-frequency signals that appear as low-frequency signals. The limit at which this occurs is a function of the number of discrete thermocouples deployed about the turbine exhaust duct. That is, the number of thermocouples in the array on the duct is insufficient to resolve all of the spatial frequencies present in the exhaust pattern established by the noted turbine components. The high spatial frequency content of the exhaust pattern is therefore incorrectly represented (aliased) as lower spatial frequency content. The aliased signal is an ambiguous one potentially representing two or more spatial frequency patterns including anomalies that may be of interest. Significant anomalies may therefore go undetected. One solution would be to deploy many more thermocouples. Such a solution is not practical, however.
The aliasing phenomenon is well known in the signal-processing field, less so in the field of turbomachinery. Nevertheless, the problem can clearly be seen through several simple equations for N number of thermocouples spaced equidistant from one another about the perimeter of an exhaust duct. The location of that thermocouple, n, with respect to the center of the exhaust duct is defined by the azimuthal angle {circle around (-)}n in the relationship set out in Equation (1):
{circle around (-)}n=2xcfx80n/Nxe2x80x83xe2x80x83Eq. (1)
For what is effectively a periodic sampling of a sinusoidal signal, the signal to be analyzed, identified generally by the function x({circle around (-)}), can be resolved and simplified into generic Equation (2), in which the amplitude of the signal is A, and k is its spatial frequency:
x({circle around (-)})=A cos(k{circle around (-)})xe2x80x83xe2x80x83Eq. (2)
When sampled at each of the N discrete locations the result is;
x(n)=A cos(2xcfx80kn/N)xe2x80x83xe2x80x83Eq. (3)
For two such spatially periodic components of differing frequencies, k1 and k2, and described by the functions x1(xcex8) and x2(xcex8), we get the two sets of sampled measurements x1(n) and x2(n), where:
x1(n)=A cos(2xcfx80k1n/N)xe2x80x83xe2x80x83Eq. (4)
and
x2(n)=A cos(2xcfx80k2n/N)xe2x80x83xe2x80x83Eq. (5)
when each of the differing signals is sampled at identical locations on the exhaust duct. It can be shown by substitution that the two sets of sampled measurements, x1(n) and x2(n), are identical when the relationship
k1xe2x88x92k2=mNxe2x80x83xe2x80x83Eq. (6)
is satisfied for some m=. . . , xe2x88x922, xe2x88x921, 0, 1, 2, . . . , etc. (i.e., any integer). In this circumstance, the two signals are indistinguishable when observed via the array of N thermocouples.
An example illustrates this point. In a gas turbine having 14 combustor cans and 27 thermocouples spaced about the exhaust duct, the exhaust pattern will contain features indicating the presence of the 14 combustor cans. However, since the sampling spread is not adequate, the features will not be accurately represented. The spatial frequencies of the fundamental (14 per revolution) and harmonics (28, 42, . . . , per revolution) exceed the Nyquist limit of 27/2=13.5 beyond which the signal cannot be uniquely represented. For the fundamental with k1=14 we have from Equation (6) k2=xe2x88x9213 with m=1. That is, the signal from the 14 combustor cans is aliased in the observable range xc2x113.5 per revolution, as a signal out of phase and with a spatial frequency of 13 per revolution. Interpretation of this aliased signal would be confusing.
For the first harmonic we have from Equation (6) k1=28 and k2=1 for m=1. That is, the signal is observed as one with a spatial frequency of 1 per revolution. This signal would likely be sufficiently strong to obscure any real discrete defect about the turbine annulus that would also be characterized by a fundamental spatial frequency of 1 per revolution.
It can be seen that signal aliasing will occur using conventional discrete thermocouple systems. As a result, significant events such as thermal distortions and the like may be masked by normal exhaust temperature patterns and remain undetected by the thermocouples of the exhaust duct. Accordingly, there is a need for a technique to describe the exhaust gas temperature profile and deviations associated therewith. That technique can be used to identify normal pattern spatial frequencies that may mask anomalies that should be detected. There is thus a need for a mechanism to eliminate or minimize the aliasing of the spatial frequencies of the normal temperature pattern. There is also a need for a sensing arrangement that resolves aliasing and thereby provides an accurate temperature profile in regard to the entirety of the turbine structure.
The above-mentioned needs are met by the present invention, which provides a methodology and set of sensor types suitable for improved turbine exhaust gas temperature measurements. The method includes limiting the bandwidth of the spectral character of an exhaust gas temperature profile of a turbine having an exhaust gas duct. It includes the steps of first determining the spatial frequencies of a gas turbine exhaust temperature pattern and then establishing a spatial frequency limit. The method further includes the step of defining a filter function to filter out those of the spatial frequencies greater than the spatial frequency limit and then applying to the turbine exhaust duct a temperature sensor system that generates the filter function.
The sensor arrangement to achieve improved exhaust gas measurements provides the appropriate filter function. One such arrangement is a sensor with a plurality of distributed gradient thermocouples affixable to the turbine exhaust duct, wherein each of the distributed gradient thermocouples is formed of two or more materials of differing thermoelectric coefficients, and wherein the sensor defines a filter function for filtering out aliased signals of a standard exhaust gas temperature pattern.
The present invention and its advantages over the prior art will become apparent upon reading the following detailed description and the appended claims with reference to the accompanying drawings.